Data Reanalysis Assignment
Andrew Mark
Preliminaries
You will need to install and launch the fallowing packages: stringr, knitr, ggplot2, ggmap, and Bchron. You will also needd to read Oreto García Puchol, Agustín Diez Castillo, and Salvador Pardo-Gordó’s paper “New insights into the neolithisation process in southwest Europe according to spatial density analysis from calibrated radiocarbon dates”, and load that into R using the curl command and import the data from Puchol et al (2017) edited data.csv and sites_iberian_peninsula_jaa.kmz.
All these packages should be launched
library(stringr)
library(Bchron)## Warning: package 'Bchron' was built under R version 3.4.2library(knitr)## Warning: package 'knitr' was built under R version 3.4.2library(ggplot2)
library(ggmap)## Warning: package 'ggmap' was built under R version 3.4.3library(curl)Paper Background
In Puchol et al’s 2017 article “New insights into the neolithisation process in southwest Europe according to spatial density analysis from calibrated radiocarbon dates,” their goal is to map the neolithisation, the transition from the Late Mesolithic to the Early Neolithic, of the Iberian Peninsula by looking at sites associated with the earliest Neolithic processes such the introduction of regular blade knapping technology, and radiocarbon dates from each site. They compiled a database with all of the known sites and radiocarbon dates in the peninsula that are within range of 8000 BP to 5500 BP.
After collecting all the data points, Puchol et al (2017) had a total of 1276 uncalibrated radiocarbon dates, they then filtered out any dates which could have been affected by the reservoir effect, or any dates which had a standard deviation of 150 years. This left them with 834 uncalibrated radiocarbon dates with a standard deviation of 59.9. They then calibrated these dates with the Bchron package in R using the IntCal13 calibration curve. Next, they binned the radiocarbon dates in groups of 200-year intervals. After that the bins were normalized and the values were fit to a smoothed Gaussian isotropic kernel using the density.ppp command from the R package spatstat. Finally, Puchol et al (2017) used the raster package and the rasterVis package to produce maps of the special and quantitative distribution of radiocarbon dates along with chronological maps representing density of radiocarbon dates.
Puchol et al (2017) discuss their paper findings by stating that through their analyses, it becomes evident that when mapping the neolithisation of Iberia a general east/west route can be suggested. There is also a gradual increase of radiocarbon dates in association with Neolithic dates starting around 7000 cal BC. Their maps also show that there seems to be some significant importance between the Mediterranean coastline and the expansion of Neolithic technology. Puchol et al Concludes the paper by suggesting that this map can help create an open debate between whether the neolithisation of Iberian was from demic diffusion, cultural diffusion, or a combination of the two.
My Reanalyses
For my reanalyses of Puchol et al (2017), I will first calculate the average standard deviation from the dataset they provide. In this article Puchol et al (2017) use 864 dates, but only provide 165 to the reader. Because if this, I will calculate the standard deviation and use an F-test to see if there is a significant difference between the stander deviation I calculate from the 165 dates compared to the 864 dates. Next, I will recreate Puchol et al’s (2017) spatial and quantitative distribution of radiocarbon dates map. Finaly, I will use calibrate the radiocarbon dates using the Bchron package which will let me calibrate the 165 radiocarbon data using the intcal13 calibration curve.
Imported Database
While I was importing the dataset into R, I noticed that the original dataset (labeled” Puchol et al (2017) original data.csv” on my GitHub data-reanalysis-assignment repository) was missing the Latitude and Longitude components for each site. These values were located in a Google Earth kmz file under supplementary materials on the original paper. I uploaded this Google Earth file to my repository and named it “sites_iberian_peninsula_jaa.kmz.” I tried to figure out a way to input the Latitude and Longitude from Google Earth directly into R, I could not and had to instead import them into the “Puchol et al (2017) original data.csv.” I then saved this as a new csv file titled “Puchol et al (2017) edited data.csv” and uploaded it to GitHub. This is the cvs file I used for the entire project.
f <- curl("https://raw.githubusercontent.com/andym5780/data-reanalysis-assignment/master/Puchol%20et%20al%20(2017)%20edited%20data.csv")
orig <- read.csv(f, header = TRUE)
head(orig)## Site.name Region Latitude Longitude Lab.Code
## 1 Abric de la Falguera Eastern / Southern 38.67278 -0.5663889 AA60627
## 2 Abric de la Falguera Eastern / Southern 38.67278 -0.5663889 Beta142289
## 3 Arenaza Cantabrian 43.27472 -3.1142167 OxA7157
## 4 Caldeirao Portugal 39.65251 -8.2480028 OxA1034
## 5 Caldeirao Portugal 39.65251 -8.2480028 OxA1035
## 6 Caldeirao Portugal 39.65251 -8.2480028 OxA1037
## Date.BP SD d13C Level Period Material.type
## 1 5655 54 NA VI Neolithic Bone
## 2 6510 80 NA 2051b Neolithic Seed/Fruit
## 3 6040 75 NA IC2 Neolithic Bone
## 4 6230 80 NA NA II Neolithic Bone
## 5 6330 80 NA NA II Neolithic Bone
## 6 5970 120 NA Type of date Context Neolithic Bone
## C14.method Reference Radiocarbon.sites
## 1 AMS Garc<ed>a Puchol et al. 2009 2
## 2 AMS Garc<ed>a Puchol et al. 2009 2
## 3 AMS Fano et al. 2015 1
## 4 AMS Rojo et al. 2012 4
## 5 AMS Rojo et al. 2012 4
## 6 Conventional Rojo et al. 2012 4Here I have brought in the edited database used by Pulchol et al (2017). They have only provided 165 dates despite the fact that they did these calculation with 834 dates because of this, there might be differenced in my results compared to theirs.
1 Testing Significant Differences in the Standard Deviations
Bellow I will test to see if there is a significant difference in the average standard deviations of the original dataset with 834 site and the average standard deviation found in this dataset with 165 dates. I will do this by using an F-test regarding two population standard deviations. I will us a right tailed test to see if the difference is significant because it would seem like if these values are different, then the standard deviation for sd1, which comes from the 834 dates, would be larger. Here my null hypothesis is sd1=sd2, and my alternative hypothesis is sd1>sd2 where sd1 comes from the 834 dates and sd2 comes from the 165 dates.
The first standard deviation, sd1, comes from within Pulchol et al (2017). They state that the average standard deviation is 59.9 so
sd1 <- 59.9Next, I will calculate the average standard deviation from the 165 dates.
x <- sum(orig$SD)
sd2 <-x/165
sd2## [1] 43.25455So the average standard deviation from 165 dates is 43.25455. Next I will conduct the F-test.
Fo <- sd1/sd2
Fo## [1] 1.384826Here our Fo test statistic is 1.384826. In order to test whether or not I should reject our null hypothesis we must see if this Fo is greater than our test statistic. Next we will calculate our critical value at a 95% confidence level, with the degrees of freedom being 833 for df1 and 164 for df2 so
df1 <- 833
df2 <- 164
cv <- qf(.95, df1=df1, df2=df2)
cv## [1] 1.229855Here the Fo is greater than cv, so we reject the null hypothesis and say that there is significant evidence to suggest that average standard deviation for the 834 dates is greater than the 165 dates at the alpha equals 0.05 level of significant, and that this can cause there to be a difference in results compared to the original paper.
2 Spatial and Quantitative Distribution of Radiocarbon Dates Map
My Spatial and Quantitative Distribution of Radiocarbon Dates Map
In this part of the project I will attempted to recreate Puchol et al’s (2017) spatial and quantitative distribution of radiocarbon dates map. Instead of using the raster and the rasterVis packages like they did, I will use the ggplot2 and ggmap. I chose to use the packages instead of the ones used by Puchol et al (2017) because the ggmap package does not require one to download a shapefile and then load it into R markdown, and because the shapefile I found that appeared to be the same as the one used by Puchol et al (2017) required me to purchase it. I tried using a similar, free to download shape file first, but it resulted in an error when I uploaded the shapefile to GitHub and then tried to use the curl command to input it into R markdown. The ggmap package uses the information from Google Maps to create maps and therefore does not require a shapefile to be downloaded.
size <- make_bbox(lon = orig$Longitude, lat = orig$Latitude, f = .1)Here I have set the parameters for how large my map will be by using the latitude and longitude from the orig dataframe. This command will make sure that the map is an appropriate size and will not produce something too large or too small.
sq_map <- get_map(location = size, maptype = "satellite", source = "google")## Warning: bounding box given to google - spatial extent only approximate.## converting bounding box to center/zoom specification. (experimental)## Map from URL : http://maps.googleapis.com/maps/api/staticmap?center=39.947204,-2.689087&zoom=6&size=640x640&scale=2&maptype=satellite&language=en-EN&sensor=falseHere the get_map command generates will retrieve a map, in this case from Google Maps because I told it to by setting source equal to “google”, and it will be a hybrid between a satellite map and a terrain map. The map will be fitted to the dimensions specified with the make_bbox command
ggmap(sq_map) + geom_point(data = orig, mapping = aes(x = orig$Longitude, y = orig$Latitude))
Here I have imported the map of the Iberian Peninsula and added the sites where the 165 radiocarbon dates were sampled from. As one can see there are not 165 individual sites because some site have multiple dates. The dataset that Puchol et al (2017) gave contains only 49 site, while their paper indicates they used 239 when conducting their study. This difference in site size may cause the spatial and quantitative distribution of radiocarbon dates map to look slightly different.
RadiocarbonDatesPerSites <- orig$Radiocarbon.sites
ggmap(sq_map) + geom_point(data = orig, mapping = aes(x = orig$Longitude, y = orig$Latitude, color = RadiocarbonDatesPerSites, size = RadiocarbonDatesPerSites))
Above is my version of the spatial and quantitative distribution of radiocarbon dates map. I set the column orig$Radiocarbon.sites equal to the variable RadiocarbonDatesPerSites so that this title would appear in the legend. By setting both color and size equal to RadiocarbonDatesPerSites in the geom_point command I was able to make it so that the color of the point and the size of the point correlates to the amount of radiocarbon dates taken from the site. Here the larger the point and the lighter the color the more radiocarbon dates were taken from the site. As you can see from the color legend the maximum number of radiocarbon dates taken from a sight was just below 15. I will now compare this to the spatial and quantitative distribution of radiocarbon dates map created by Puchol et al (2017).
Puchol et al (2017) Spatial and Quantitative Distribution of Radiocarbon Dates Map
The first noticeable difference is the color differences between the maps. This is because Puchol et al (2017) used a personally downloaded shapefile and the raster and rasterVis packages as I have mentioned earlier. The next major difference is that my map has less points then their map does. This is due to the fact that Puchol et al (2017) only provided 165 date correlating to 49 site. This has also been discussed earlier. The final difference is the size of my points compared to Puchol et al (2017). Some of the largest points on my map are the smaller points on their map. This is again due to the lack of sites Puchol et al (2017) included in the supplementary dataset. In their data, highest ratio of radiocarbon dates to site was 14 while in the dataset used by Puchol et al (2017) when they generated their map it appears to be around 33. Therefore my highest ratio is only halfway to their ratio which is why my largest points are some of their smaller points. Besides these small differences the maps are quite similar and can effective by considered the same map just with different amounts of data points.
3 Calibrating the Radiocarbon Dates
Next I will calibrate the 165 radiocarbon
orig$CalibrationCurvesUsed <- "intcal13"Here I have created a new columns in the dataset so that I can used the columns to calculate the calibration curve instead of writing out intcal13 165 times when I am calibrating the dates
head(orig)## Site.name Region Latitude Longitude Lab.Code
## 1 Abric de la Falguera Eastern / Southern 38.67278 -0.5663889 AA60627
## 2 Abric de la Falguera Eastern / Southern 38.67278 -0.5663889 Beta142289
## 3 Arenaza Cantabrian 43.27472 -3.1142167 OxA7157
## 4 Caldeirao Portugal 39.65251 -8.2480028 OxA1034
## 5 Caldeirao Portugal 39.65251 -8.2480028 OxA1035
## 6 Caldeirao Portugal 39.65251 -8.2480028 OxA1037
## Date.BP SD d13C Level Period Material.type
## 1 5655 54 NA VI Neolithic Bone
## 2 6510 80 NA 2051b Neolithic Seed/Fruit
## 3 6040 75 NA IC2 Neolithic Bone
## 4 6230 80 NA NA II Neolithic Bone
## 5 6330 80 NA NA II Neolithic Bone
## 6 5970 120 NA Type of date Context Neolithic Bone
## C14.method Reference Radiocarbon.sites
## 1 AMS Garc<ed>a Puchol et al. 2009 2
## 2 AMS Garc<ed>a Puchol et al. 2009 2
## 3 AMS Fano et al. 2015 1
## 4 AMS Rojo et al. 2012 4
## 5 AMS Rojo et al. 2012 4
## 6 Conventional Rojo et al. 2012 4
## CalibrationCurvesUsed
## 1 intcal13
## 2 intcal13
## 3 intcal13
## 4 intcal13
## 5 intcal13
## 6 intcal13Above this you can see that a new column named CalibrationCurvesUsed has been added. It which contains the words incal13 in every row, and this will be the calibration curve used for the radiocarbon dates.
ages2 = BchronCalibrate(ages=orig$Date.BP
,ageSds=orig$SD, calCurves= orig$CalibrationCurvesUsed)Here I have calibrated the radiocarbon dates using the BchronCalibrate command
Below is a list of all of the 165 calibrated radiocarbon dates and the 95% Highest density regions. These are the regions which are most likely to contain the true date.
By calibrating all of the radiocarbon dates, Puchol et al (2017) were able to then create multiple density maps spanning from 7400 to 4200 cal BC. This allowed them to then make general assumptions about the neolithisation of Iberia. If they provided my with the 834 dates and 239 sites I would try to recreate some of these density maps, but with the 165 dates and 49 sites my maps would look nothing like theirs. While it is helpful that they provided some of their data and preformed all of their calculations in R, it would be more helpful if they provided all of their data so that others to run their experiments. Below are the calibrated dates.
summary(ages2)## 95% Highest density regions for Date1
## $`94.3%`
## [1] 6309 6558
##
##
## 95% Highest density regions for Date2
## $`76.9%`
## [1] 7274 7520
##
## $`17.5%`
## [1] 7533 7563
##
##
## 95% Highest density regions for Date3
## $`51.9%`
## [1] 6730 7032
##
## $`18.1%`
## [1] 7040 7088
##
## $`24.7%`
## [1] 7093 7155
##
##
## 95% Highest density regions for Date4
## $`94.6%`
## [1] 6938 7314
##
##
## 95% Highest density regions for Date5
## $`2.8%`
## [1] 7026 7059
##
## $`4.8%`
## [1] 7062 7115
##
## $`86.9%`
## [1] 7154 7422
##
##
## 95% Highest density regions for Date6
## $`94.7%`
## [1] 6538 7156
##
##
## 95% Highest density regions for Date7
## $`94.5%`
## [1] 6495 6881
##
##
## 95% Highest density regions for Date8
## $`3.8%`
## [1] 7027 7058
##
## $`6.4%`
## [1] 7067 7113
##
## $`84%`
## [1] 7155 7266
##
##
## 95% Highest density regions for Date9
## $`94.4%`
## [1] 7260 7421
##
##
## 95% Highest density regions for Date10
## $`1%`
## [1] 7280 7282
##
## $`93.4%`
## [1] 7286 7420
##
##
## 95% Highest density regions for Date11
## $`36.7%`
## [1] 7266 7341
##
## $`57.5%`
## [1] 7348 7415
##
##
## 95% Highest density regions for Date12
## $`29.2%`
## [1] 7256 7337
##
## $`64.8%`
## [1] 7352 7414
##
##
## 95% Highest density regions for Date13
## $`94.3%`
## [1] 7263 7421
##
##
## 95% Highest density regions for Date14
## $`93.6%`
## [1] 7569 7667
##
##
## 95% Highest density regions for Date15
## $`3.8%`
## [1] 7179 7215
##
## $`42.8%`
## [1] 7241 7330
##
## $`16.7%`
## [1] 7358 7370
##
## $`30%`
## [1] 7392 7411
##
##
## 95% Highest density regions for Date16
## $`93.9%`
## [1] 7169 7312
##
##
## 95% Highest density regions for Date17
## $`40.2%`
## [1] 7012 7128
##
## $`54%`
## [1] 7145 7250
##
##
## 95% Highest density regions for Date18
## $`93.7%`
## [1] 6313 6442
##
##
## 95% Highest density regions for Date19
## $`85.9%`
## [1] 7687 7855
##
## $`8.3%`
## [1] 7905 7915
##
##
## 95% Highest density regions for Date20
## $`93.4%`
## [1] 7318 7458
##
##
## 95% Highest density regions for Date21
## $`0.4%`
## [1] 7033 7039
##
## $`0.2%`
## [1] 7089 7092
##
## $`93.4%`
## [1] 7157 7303
##
##
## 95% Highest density regions for Date22
## $`64.8%`
## [1] 6996 7180
##
## $`29.5%`
## [1] 7194 7242
##
##
## 95% Highest density regions for Date23
## $`64.8%`
## [1] 6996 7180
##
## $`29.5%`
## [1] 7194 7242
##
##
## 95% Highest density regions for Date24
## $`65.9%`
## [1] 7429 7514
##
## $`28.1%`
## [1] 7538 7560
##
##
## 95% Highest density regions for Date25
## $`58.4%`
## [1] 7325 7400
##
## $`34.1%`
## [1] 7410 7428
##
##
## 95% Highest density regions for Date26
## $`94.5%`
## [1] 6401 6657
##
##
## 95% Highest density regions for Date27
## $`83.7%`
## [1] 6744 6914
##
## $`10.7%`
## [1] 6916 6929
##
##
## 95% Highest density regions for Date28
## $`34.9%`
## [1] 6739 6809
##
## $`48.5%`
## [1] 6811 6859
##
## $`10.4%`
## [1] 6872 6879
##
##
## 95% Highest density regions for Date29
## $`94.4%`
## [1] 6974 7160
##
##
## 95% Highest density regions for Date30
## $`94.5%`
## [1] 6950 7160
##
##
## 95% Highest density regions for Date31
## $`94.4%`
## [1] 6994 7161
##
##
## 95% Highest density regions for Date32
## $`94.3%`
## [1] 6494 6669
##
##
## 95% Highest density regions for Date33
## $`27.3%`
## [1] 7019 7124
##
## $`66.8%`
## [1] 7150 7256
##
##
## 95% Highest density regions for Date34
## $`94.1%`
## [1] 7439 7565
##
##
## 95% Highest density regions for Date35
## $`52.6%`
## [1] 7326 7399
##
## $`39.3%`
## [1] 7411 7430
##
##
## 95% Highest density regions for Date36
## $`90.9%`
## [1] 7161 7294
##
## $`3.1%`
## [1] 7298 7300
##
##
## 95% Highest density regions for Date37
## $`60.4%`
## [1] 7170 7329
##
## $`12.1%`
## [1] 7358 7370
##
## $`21.2%`
## [1] 7394 7411
##
##
## 95% Highest density regions for Date38
## $`64.8%`
## [1] 6996 7180
##
## $`29.5%`
## [1] 7194 7242
##
##
## 95% Highest density regions for Date39
## $`86.9%`
## [1] 6970 7327
##
## $`1%`
## [1] 7364 7365
##
## $`6.7%`
## [1] 7397 7410
##
##
## 95% Highest density regions for Date40
## $`83.2%`
## [1] 6996 7328
##
## $`3.2%`
## [1] 7361 7366
##
## $`8%`
## [1] 7396 7410
##
##
## 95% Highest density regions for Date41
## $`9%`
## [1] 7026 7115
##
## $`48.8%`
## [1] 7154 7343
##
## $`36.6%`
## [1] 7347 7416
##
##
## 95% Highest density regions for Date42
## $`16.9%`
## [1] 6319 6376
##
## $`76.7%`
## [1] 6386 6474
##
##
## 95% Highest density regions for Date43
## $`34.8%`
## [1] 7265 7339
##
## $`59.2%`
## [1] 7349 7415
##
##
## 95% Highest density regions for Date44
## $`41%`
## [1] 7270 7343
##
## $`53.4%`
## [1] 7347 7416
##
##
## 95% Highest density regions for Date45
## $`0.9%`
## [1] 7280 7282
##
## $`93.4%`
## [1] 7287 7419
##
##
## 95% Highest density regions for Date46
## $`6.9%`
## [1] 7329 7361
##
## $`9.6%`
## [1] 7366 7395
##
## $`74.9%`
## [1] 7412 7476
##
##
## 95% Highest density regions for Date47
## $`67.9%`
## [1] 6996 7334
##
## $`11.4%`
## [1] 7354 7378
##
## $`15.2%`
## [1] 7382 7414
##
##
## 95% Highest density regions for Date48
## $`21.2%`
## [1] 7325 7402
##
## $`71.7%`
## [1] 7407 7487
##
##
## 95% Highest density regions for Date49
## $`0.5%`
## [1] 7031 7041
##
## $`0.1%`
## [1] 7074 7075
##
## $`0.4%`
## [1] 7088 7094
##
## $`93.4%`
## [1] 7156 7425
##
##
## 95% Highest density regions for Date50
## $`0.8%`
## [1] 6568 6586
##
## $`0.2%`
## [1] 6604 6607
##
## $`61.1%`
## [1] 6619 7030
##
## $`9.8%`
## [1] 7042 7073
##
## $`3.7%`
## [1] 7076 7087
##
## $`19.1%`
## [1] 7095 7154
##
##
## 95% Highest density regions for Date51
## $`76.9%`
## [1] 7259 7524
##
## $`17.5%`
## [1] 7529 7564
##
##
## 95% Highest density regions for Date52
## $`94.5%`
## [1] 6960 7165
##
##
## 95% Highest density regions for Date53
## $`0.6%`
## [1] 7280 7281
##
## $`93.6%`
## [1] 7287 7421
##
##
## 95% Highest density regions for Date54
## $`36.1%`
## [1] 7265 7340
##
## $`58.2%`
## [1] 7348 7415
##
##
## 95% Highest density regions for Date55
## $`94.4%`
## [1] 6985 7167
##
##
## 95% Highest density regions for Date56
## $`3.8%`
## [1] 7028 7056
##
## $`1.7%`
## [1] 7068 7079
##
## $`5%`
## [1] 7081 7112
##
## $`83.4%`
## [1] 7156 7257
##
##
## 95% Highest density regions for Date57
## $`81.5%`
## [1] 6797 7011
##
## $`12.7%`
## [1] 7129 7144
##
##
## 95% Highest density regions for Date58
## $`1.5%`
## [1] 6797 6819
##
## $`65.9%`
## [1] 6828 7024
##
## $`26.8%`
## [1] 7117 7152
##
##
## 95% Highest density regions for Date59
## $`94.1%`
## [1] 6302 6437
##
##
## 95% Highest density regions for Date60
## $`83%`
## [1] 6297 6414
##
## $`11.1%`
## [1] 6423 6434
##
##
## 95% Highest density regions for Date61
## $`94.2%`
## [1] 6793 6994
##
##
## 95% Highest density regions for Date62
## $`94.1%`
## [1] 6302 6437
##
##
## 95% Highest density regions for Date63
## $`94.5%`
## [1] 7278 7417
##
##
## 95% Highest density regions for Date64
## $`94.6%`
## [1] 6956 7162
##
##
## 95% Highest density regions for Date65
## $`90.2%`
## [1] 7001 7174
##
## $`4%`
## [1] 7225 7229
##
##
## 95% Highest density regions for Date66
## $`0.5%`
## [1] 6863 6867
##
## $`27%`
## [1] 6882 7032
##
## $`22%`
## [1] 7040 7088
##
## $`44.7%`
## [1] 7092 7155
##
##
## 95% Highest density regions for Date67
## $`17.7%`
## [1] 7024 7117
##
## $`76.4%`
## [1] 7153 7261
##
##
## 95% Highest density regions for Date68
## $`94.5%`
## [1] 6958 7171
##
##
## 95% Highest density regions for Date69
## $`94.3%`
## [1] 7003 7163
##
##
## 95% Highest density regions for Date70
## $`94.4%`
## [1] 6985 7169
##
##
## 95% Highest density regions for Date71
## $`86.9%`
## [1] 6990 7175
##
## $`7.4%`
## [1] 7222 7232
##
##
## 95% Highest density regions for Date72
## $`72.5%`
## [1] 6997 7178
##
## $`2.6%`
## [1] 7205 7208
##
## $`19.3%`
## [1] 7211 7239
##
##
## 95% Highest density regions for Date73
## $`3.7%`
## [1] 6798 6819
##
## $`90.5%`
## [1] 6831 6994
##
##
## 95% Highest density regions for Date74
## $`64.8%`
## [1] 6996 7180
##
## $`29.5%`
## [1] 7194 7242
##
##
## 95% Highest density regions for Date75
## $`94.5%`
## [1] 6971 7164
##
##
## 95% Highest density regions for Date76
## $`66%`
## [1] 6661 6802
##
## $`28.1%`
## [1] 6814 6847
##
##
## 95% Highest density regions for Date77
## $`30.6%`
## [1] 6891 7032
##
## $`20.6%`
## [1] 7039 7088
##
## $`43.1%`
## [1] 7092 7155
##
##
## 95% Highest density regions for Date78
## $`94.4%`
## [1] 6940 7160
##
##
## 95% Highest density regions for Date79
## $`94.5%`
## [1] 6935 7165
##
##
## 95% Highest density regions for Date80
## $`2.2%`
## [1] 6750 6767
##
## $`92.1%`
## [1] 6773 6975
##
##
## 95% Highest density regions for Date81
## $`69.9%`
## [1] 7005 7178
##
## $`2.7%`
## [1] 7205 7208
##
## $`21.5%`
## [1] 7211 7239
##
##
## 95% Highest density regions for Date82
## $`94.2%`
## [1] 7000 7173
##
##
## 95% Highest density regions for Date83
## $`36.8%`
## [1] 7014 7127
##
## $`57.2%`
## [1] 7147 7245
##
##
## 95% Highest density regions for Date84
## $`35.7%`
## [1] 7009 7130
##
## $`22.5%`
## [1] 7143 7184
##
## $`35.9%`
## [1] 7188 7244
##
##
## 95% Highest density regions for Date85
## $`1.7%`
## [1] 7029 7044
##
## $`1%`
## [1] 7047 7055
##
## $`1.1%`
## [1] 7069 7078
##
## $`3.1%`
## [1] 7086 7110
##
## $`87%`
## [1] 7156 7259
##
##
## 95% Highest density regions for Date86
## $`1.3%`
## [1] 7030 7043
##
## $`0.6%`
## [1] 7050 7055
##
## $`0.8%`
## [1] 7070 7077
##
## $`2.8%`
## [1] 7086 7110
##
## $`88.5%`
## [1] 7156 7260
##
##
## 95% Highest density regions for Date87
## $`62.7%`
## [1] 7173 7329
##
## $`8.4%`
## [1] 7360 7367
##
## $`22.5%`
## [1] 7395 7411
##
##
## 95% Highest density regions for Date88
## $`93.6%`
## [1] 7321 7429
##
##
## 95% Highest density regions for Date89
## $`61.2%`
## [1] 7431 7521
##
## $`32.7%`
## [1] 7532 7563
##
##
## 95% Highest density regions for Date90
## $`86.4%`
## [1] 7164 7294
##
## $`7.6%`
## [1] 7296 7302
##
##
## 95% Highest density regions for Date91
## $`94.2%`
## [1] 6748 6908
##
##
## 95% Highest density regions for Date92
## $`94.3%`
## [1] 6964 7157
##
##
## 95% Highest density regions for Date93
## $`94.2%`
## [1] 6793 6994
##
##
## 95% Highest density regions for Date94
## $`31.6%`
## [1] 6893 7029
##
## $`2.1%`
## [1] 7045 7048
##
## $`8.7%`
## [1] 7056 7069
##
## $`6.9%`
## [1] 7078 7085
##
## $`44.7%`
## [1] 7111 7154
##
##
## 95% Highest density regions for Date95
## $`94.3%`
## [1] 6967 7157
##
##
## 95% Highest density regions for Date96
## $`93.8%`
## [1] 7167 7308
##
##
## 95% Highest density regions for Date97
## $`88.4%`
## [1] 7317 7507
##
## $`5.3%`
## [1] 7547 7550
##
##
## 95% Highest density regions for Date98
## $`94.1%`
## [1] 7293 7428
##
##
## 95% Highest density regions for Date99
## $`0.5%`
## [1] 7342 7346
##
## $`74.6%`
## [1] 7418 7509
##
## $`17.8%`
## [1] 7545 7553
##
##
## 95% Highest density regions for Date100
## $`0.8%`
## [1] 7029 7044
##
## $`0.5%`
## [1] 7047 7055
##
## $`0.5%`
## [1] 7069 7078
##
## $`1.4%`
## [1] 7086 7110
##
## $`81.6%`
## [1] 7156 7326
##
## $`9.3%`
## [1] 7399 7409
##
##
## 95% Highest density regions for Date101
## $`30.6%`
## [1] 6891 7032
##
## $`20.6%`
## [1] 7039 7088
##
## $`43.1%`
## [1] 7092 7155
##
##
## 95% Highest density regions for Date102
## $`55.4%`
## [1] 6788 7029
##
## $`1.5%`
## [1] 7045 7047
##
## $`6.9%`
## [1] 7056 7068
##
## $`4%`
## [1] 7079 7085
##
## $`26.5%`
## [1] 7111 7154
##
##
## 95% Highest density regions for Date103
## $`0.8%`
## [1] 6803 6813
##
## $`39.1%`
## [1] 6848 7029
##
## $`15.7%`
## [1] 7044 7069
##
## $`5.1%`
## [1] 7078 7085
##
## $`0.7%`
## [1] 7100 7100
##
## $`32.9%`
## [1] 7110 7154
##
##
## 95% Highest density regions for Date104
## $`1.5%`
## [1] 6797 6819
##
## $`65.9%`
## [1] 6828 7024
##
## $`26.8%`
## [1] 7117 7152
##
##
## 95% Highest density regions for Date105
## $`94.1%`
## [1] 6290 6402
##
##
## 95% Highest density regions for Date106
## $`31.1%`
## [1] 7023 7119
##
## $`62.6%`
## [1] 7152 7248
##
##
## 95% Highest density regions for Date107
## $`1.3%`
## [1] 7030 7043
##
## $`0.2%`
## [1] 7054 7055
##
## $`0.8%`
## [1] 7070 7077
##
## $`2.8%`
## [1] 7086 7110
##
## $`88.6%`
## [1] 7156 7257
##
##
## 95% Highest density regions for Date108
## $`69.4%`
## [1] 6960 7181
##
## $`25.1%`
## [1] 7194 7242
##
##
## 95% Highest density regions for Date109
## $`78.7%`
## [1] 6995 7177
##
## $`15.6%`
## [1] 7216 7238
##
##
## 95% Highest density regions for Date110
## $`1.2%`
## [1] 7029 7044
##
## $`0.8%`
## [1] 7046 7055
##
## $`0.8%`
## [1] 7069 7078
##
## $`2.2%`
## [1] 7086 7110
##
## $`89%`
## [1] 7156 7271
##
##
## 95% Highest density regions for Date111
## $`94.5%`
## [1] 6960 7165
##
##
## 95% Highest density regions for Date112
## $`94.5%`
## [1] 6982 7160
##
##
## 95% Highest density regions for Date113
## $`1.9%`
## [1] 6913 6924
##
## $`21.6%`
## [1] 6926 7032
##
## $`22.7%`
## [1] 7040 7088
##
## $`47.9%`
## [1] 7093 7155
##
##
## 95% Highest density regions for Date114
## $`94.4%`
## [1] 6993 7165
##
##
## 95% Highest density regions for Date115
## $`94.2%`
## [1] 6937 7156
##
##
## 95% Highest density regions for Date116
## $`94.4%`
## [1] 6954 7155
##
##
## 95% Highest density regions for Date117
## $`87.4%`
## [1] 6673 7011
##
## $`7.1%`
## [1] 7129 7144
##
##
## 95% Highest density regions for Date118
## $`3.4%`
## [1] 7026 7059
##
## $`6%`
## [1] 7063 7115
##
## $`84.9%`
## [1] 7154 7310
##
##
## 95% Highest density regions for Date119
## $`91.9%`
## [1] 6554 6748
##
## $`2.1%`
## [1] 6769 6770
##
##
## 95% Highest density regions for Date120
## $`94.2%`
## [1] 7435 7612
##
##
## 95% Highest density regions for Date121
## $`94.5%`
## [1] 6968 7159
##
##
## 95% Highest density regions for Date122
## $`94.4%`
## [1] 6998 7163
##
##
## 95% Highest density regions for Date123
## $`0.5%`
## [1] 7184 7189
##
## $`32.6%`
## [1] 7246 7332
##
## $`24.4%`
## [1] 7356 7373
##
## $`35.7%`
## [1] 7390 7412
##
##
## 95% Highest density regions for Date124
## $`25.9%`
## [1] 7011 7129
##
## $`68.5%`
## [1] 7144 7267
##
##
## 95% Highest density regions for Date125
## $`32.3%`
## [1] 7008 7131
##
## $`62.1%`
## [1] 7141 7262
##
##
## 95% Highest density regions for Date126
## $`25.9%`
## [1] 7011 7129
##
## $`68.5%`
## [1] 7144 7267
##
##
## 95% Highest density regions for Date127
## $`68.1%`
## [1] 7160 7329
##
## $`9.8%`
## [1] 7358 7370
##
## $`16.2%`
## [1] 7394 7411
##
##
## 95% Highest density regions for Date128
## $`0.6%`
## [1] 6805 6812
##
## $`93.9%`
## [1] 6851 7164
##
##
## 95% Highest density regions for Date129
## $`94.5%`
## [1] 6968 7255
##
##
## 95% Highest density regions for Date130
## $`0.9%`
## [1] 7444 7449
##
## $`93.2%`
## [1] 7458 7590
##
##
## 95% Highest density regions for Date131
## $`0.1%`
## [1] 7295 7295
##
## $`93.9%`
## [1] 7306 7431
##
##
## 95% Highest density regions for Date132
## $`88.2%`
## [1] 6313 6678
##
## $`2.6%`
## [1] 6684 6690
##
## $`3.8%`
## [1] 6705 6714
##
##
## 95% Highest density regions for Date133
## $`83.9%`
## [1] 6794 7178
##
## $`0.7%`
## [1] 7205 7206
##
## $`10.1%`
## [1] 7211 7239
##
##
## 95% Highest density regions for Date134
## $`25.9%`
## [1] 7011 7129
##
## $`68.5%`
## [1] 7144 7267
##
##
## 95% Highest density regions for Date135
## $`31.4%`
## [1] 6895 7032
##
## $`21%`
## [1] 7039 7088
##
## $`41.9%`
## [1] 7092 7155
##
##
## 95% Highest density regions for Date136
## $`30.3%`
## [1] 6906 7034
##
## $`64.1%`
## [1] 7036 7155
##
##
## 95% Highest density regions for Date137
## $`1.6%`
## [1] 6799 6818
##
## $`0.5%`
## [1] 6833 6838
##
## $`38.5%`
## [1] 6842 7029
##
## $`14.5%`
## [1] 7044 7069
##
## $`5.9%`
## [1] 7077 7086
##
## $`3%`
## [1] 7098 7102
##
## $`30.4%`
## [1] 7107 7154
##
##
## 95% Highest density regions for Date138
## $`0.1%`
## [1] 6810 6810
##
## $`1.5%`
## [1] 6859 6871
##
## $`92.7%`
## [1] 6880 7155
##
##
## 95% Highest density regions for Date139
## $`30.4%`
## [1] 7013 7127
##
## $`63.8%`
## [1] 7146 7259
##
##
## 95% Highest density regions for Date140
## $`30.3%`
## [1] 6906 7034
##
## $`64.1%`
## [1] 7036 7155
##
##
## 95% Highest density regions for Date141
## $`15.9%`
## [1] 7022 7121
##
## $`78.3%`
## [1] 7152 7268
##
##
## 95% Highest density regions for Date142
## $`88.9%`
## [1] 7161 7324
##
## $`5.1%`
## [1] 7402 7406
##
##
## 95% Highest density regions for Date143
## $`0.8%`
## [1] 6803 6813
##
## $`39.1%`
## [1] 6848 7029
##
## $`15.7%`
## [1] 7044 7069
##
## $`5.1%`
## [1] 7078 7085
##
## $`0.7%`
## [1] 7100 7100
##
## $`32.9%`
## [1] 7110 7154
##
##
## 95% Highest density regions for Date144
## $`94.5%`
## [1] 6940 7166
##
##
## 95% Highest density regions for Date145
## $`0.2%`
## [1] 6759 6761
##
## $`61.6%`
## [1] 6782 7027
##
## $`5.8%`
## [1] 7058 7067
##
## $`0.6%`
## [1] 7080 7080
##
## $`26.2%`
## [1] 7112 7154
##
##
## 95% Highest density regions for Date146
## $`0.6%`
## [1] 6806 6811
##
## $`32%`
## [1] 6854 7032
##
## $`22.9%`
## [1] 7040 7088
##
## $`38.9%`
## [1] 7093 7155
##
##
## 95% Highest density regions for Date147
## $`94.5%`
## [1] 6896 7160
##
##
## 95% Highest density regions for Date148
## $`0.7%`
## [1] 6914 6919
##
## $`93.8%`
## [1] 6927 7162
##
##
## 95% Highest density regions for Date149
## $`94.2%`
## [1] 6795 6944
##
##
## 95% Highest density regions for Date150
## $`26.8%`
## [1] 6953 7033
##
## $`23.3%`
## [1] 7037 7089
##
## $`44.2%`
## [1] 7091 7155
##
##
## 95% Highest density regions for Date151
## $`94.3%`
## [1] 7432 7566
##
##
## 95% Highest density regions for Date152
## $`94.1%`
## [1] 6290 6402
##
##
## 95% Highest density regions for Date153
## $`94.1%`
## [1] 6302 6437
##
##
## 95% Highest density regions for Date154
## $`94.3%`
## [1] 7432 7566
##
##
## 95% Highest density regions for Date155
## $`8.2%`
## [1] 7512 7541
##
## $`85.2%`
## [1] 7558 7659
##
##
## 95% Highest density regions for Date156
## $`2.9%`
## [1] 6414 6428
##
## $`56.5%`
## [1] 6432 6572
##
## $`34.8%`
## [1] 6581 6630
##
##
## 95% Highest density regions for Date157
## $`94.3%`
## [1] 6451 6642
##
##
## 95% Highest density regions for Date158
## $`24.7%`
## [1] 7025 7116
##
## $`68.9%`
## [1] 7154 7249
##
##
## 95% Highest density regions for Date159
## $`24.7%`
## [1] 7025 7116
##
## $`68.9%`
## [1] 7154 7249
##
##
## 95% Highest density regions for Date160
## $`19.3%`
## [1] 7007 7132
##
## $`75.1%`
## [1] 7141 7309
##
##
## 95% Highest density regions for Date161
## $`94.5%`
## [1] 7004 7164
##
##
## 95% Highest density regions for Date162
## $`94.1%`
## [1] 6794 6967
##
##
## 95% Highest density regions for Date163
## $`94.2%`
## [1] 6786 6978
##
##
## 95% Highest density regions for Date164
## $`7.4%`
## [1] 7176 7222
##
## $`30.2%`
## [1] 7234 7334
##
## $`22.5%`
## [1] 7354 7377
##
## $`33.6%`
## [1] 7383 7413
##
##
## 95% Highest density regions for Date165
## $`94.5%`
## [1] 7273 7418